74 results on '"Ouannas, Adel"'
Search Results
2. Special Fractional-Order Map and Its Realization.
- Author
-
Khennaoui, Amina-Aicha, Ouannas, Adel, Momani, Shaher, Almatroud, Othman Abdullah, Al-Sawalha, Mohammed Mossa, Boulaaras, Salah Mahmoud, and Pham, Viet-Thanh
- Subjects
- *
LYAPUNOV exponents , *DIFFERENCE operators , *BIFURCATION diagrams , *SYSTEM dynamics - Abstract
Recent works have focused the analysis of chaotic phenomena in fractional discrete memristor. However, most of the papers have been related to simulated results on the system dynamics rather than on their hardware implementations. This work reports the implementation of a new chaotic fractional memristor map with "hidden attractors". The fractional memristor map is developed based on a memristive map by using the Grunwald–Letnikov difference operator. The fractional memristor map has flexible fixed points depending on a system's parameters. We study system dynamics for different values of the fractional orders by using bifurcation diagrams, phase portraits, Lyapunov exponents, and the 0–1 test. We see that the fractional map generates rich dynamical behavior, including coexisting hidden dynamics and initial offset boosting. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
3. The Effect of Caputo Fractional Variable Difference Operator on a Discrete-Time Hopfield Neural Network with Non-Commensurate Order.
- Author
-
Karoun, Rabia Chaimaà, Ouannas, Adel, Horani, Mohammed Al, and Grassi, Giuseppe
- Subjects
- *
HOPFIELD networks , *DIFFERENCE operators , *LYAPUNOV exponents , *FRACTIONAL calculus - Abstract
In this work, we recall some definitions on fractional calculus with discrete-time. Then, we introduce a discrete-time Hopfield neural network (D.T.H.N.N) with non-commensurate fractional variable-order (V.O) for three neurons. After that, phase-plot portraits, bifurcation and Lyapunov exponents diagrams are employed to verify that the proposed discrete time Hopfield neural network with non-commensurate fractional variable order has chaotic behavior. Furthermore, we use the 0-1 test and C 0 complexity algorithm to confirm and prove the results obtained about the presence of chaos. Finally, simulations are carried out in Matlab to illustrate the results. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
4. The Discrete Fractional Variable-Order Tinkerbell Map: Chaos, 0–1 Test, and Entropy.
- Author
-
Bensid Ahmed, Souad, Ouannas, Adel, Al Horani, Mohammed, and Grassi, Giuseppe
- Subjects
- *
ENTROPY , *CHAOS synchronization - Abstract
The dynamics of the Caputo-fractional variable-order difference form of the Tinkerbell map are studied. The phase portraits, bifurcation, and largest Lyapunov exponent (LLE) were employed to demonstrate the presence of chaos over a different fractional variable-order and establish the nature of the dynamics. In addition, the 0–1 test tool was used to detect chaos. Finally, the numerical results were confirmed using the approximate entropy. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
5. A Novel Fractional-Order Discrete SIR Model for Predicting COVID-19 Behavior.
- Author
-
Djenina, Noureddine, Ouannas, Adel, Batiha, Iqbal M., Grassi, Giuseppe, Oussaeif, Taki-Eddine, and Momani, Shaher
- Subjects
- *
BASIC reproduction number , *COVID-19 pandemic - Abstract
During the broadcast of Coronavirus across the globe, many mathematicians made several mathematical models. This was, of course, in order to understand the forecast and behavior of this epidemic's spread precisely. Nevertheless, due to the lack of much information about it, the application of many models has become difficult in reality and sometimes impossible, unlike the simple SIR model. In this work, a simple, novel fractional-order discrete model is proposed in order to study the behavior of the COVID-19 epidemic. Such a model has shown its ability to adapt to the periodic change in the number of infections. The existence and uniqueness of the solution for the proposed model are examined with the help of the Picard Lindelöf method. Some theoretical results are established in view of the connection between the stability of the fixed points of this model and the basic reproduction number. Several numerical simulations are performed to verify the gained results. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
6. Chaos in Cancer Tumor Growth Model with Commensurate and Incommensurate Fractional-Order Derivatives.
- Author
-
Debbouche, Nadjette, Ouannas, Adel, Grassi, Giuseppe, Al-Hussein, Abdul-Basset A., Tahir, Fadhil Rahma, Saad, Khaled M., Jahanshahi, Hadi, and Aly, Ayman A.
- Subjects
- *
TUMOR growth , *LYAPUNOV exponents , *BIFURCATION diagrams , *SYSTEM dynamics , *DIFFERENTIAL equations , *LORENZ equations - Abstract
Analyzing the dynamics of tumor-immune systems can play an important role in the fight against cancer, since it can foster the development of more effective medical treatments. This paper was aimed at making a contribution to the study of tumor-immune dynamics by presenting a new model of cancer growth based on fractional-order differential equations. By investigating the system dynamics, the manuscript highlights the chaotic behaviors of the proposed cancer model for both the commensurate and the incommensurate cases. Bifurcation diagrams, the Lyapunov exponents, and phase plots confirm the effectiveness of the conceived approach. Finally, some considerations regarding the biological meaning of the obtained results are reported through the manuscript. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
7. On the Stability of Incommensurate h -Nabla Fractional-Order Difference Systems.
- Author
-
Djenina, Noureddine, Ouannas, Adel, Oussaeif, Taki-Eddine, Grassi, Giuseppe, Batiha, Iqbal M., Momani, Shaher, and Albadarneh, Ramzi B.
- Subjects
- *
NONLINEAR analysis - Abstract
This work aims to present a study on the stability analysis of linear and nonlinear incommensurate h-nabla fractional-order difference systems. Several theoretical results are inferred with the help of using some theoretical schemes, such as the Z-transform method, Cauchy–Hadamard theorem, Taylor development approach, final-value theorem and Banach fixed point theorem. These results are verified numerically via two illustrative numerical examples that show the stabilities of the solutions of systems at hand. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
8. Hyperchaotic fractional Grassi–Miller map and its hardware implementation.
- Author
-
Ouannas, Adel, Khennaoui, Amina Aicha, Oussaeif, Taki-Eddine, Pham, Viet-Thanh, Grassi, Giuseppe, and Dibi, Zohir
- Subjects
- *
DIFFERENCE operators , *DIFFERENCE equations , *LYAPUNOV exponents , *DISCRETE systems , *SYSTEM dynamics , *BIFURCATION diagrams - Abstract
Most of the papers published so far on fractional discrete systems are related to theoretical results on their chaotic behaviors or to applications based on the mathematical modeling of the chaotic phenomena. No paper has been published to date regarding the hardware implementation of hyperchaotic fractional maps. This manuscript makes a contribution to the topic by presenting the first example of hardware implementation of hyperchaotic fractional maps. In particular, by exploiting the Grunwald–Letnikov difference operator, the paper introduces a new version of the fractional Grassi–Miller map. The system dynamics are analyzed via bifurcation diagrams and Lyapunov exponents, showing that the conceived map is hyperchaotic when the fractional order μ belongs to the interval [ 0. 966 , 1 ]. Finally, a hardware implementation of the fractional map is illustrated, with the aim to concretely highlight the presence of hyperchaos in physical systems described by fractional difference equations. Arduino, an open-source platform, has been used to illustrate the simplicity as well as the feasibility of the implementation. • A new version of the fractional Grassi–Miller map is introduced. • We discover system's dynamics by using phase portraits, bifurcation diagrams, and Lyapunov exponents. • Hyperchaotic behaviors are investigated. • The hardware implementation of the fractional map is reported. [ABSTRACT FROM AUTHOR]
- Published
- 2021
- Full Text
- View/download PDF
9. Finite-time stabilization of a perturbed chaotic finance model.
- Author
-
Ahmad, Israr, Ouannas, Adel, Shafiq, Muhammad, Pham, Viet-Thanh, and Baleanu, Dumitru
- Subjects
- *
DYNAMICAL systems , *STABILITY theory , *LYAPUNOV stability , *LYAPUNOV exponents , *MATHEMATICAL analysis , *BIFURCATION diagrams , *ROBUST control , *CHAOTIC communication - Abstract
[Display omitted] • This article proposes a new robust nonlinear controller that stabilizes a chaotic finance system in a finite-time without cancellation of the spacecraft's nonlinear terms, it improves the efficiency of the closed-loop. • It accomplishes an oscillation-free faster convergence of the perturbed state variables to the desired steady-state. • The proposed controller is insensitive to the parameter uncertainties of the nonlinear terms and exogenous disturbances. • The paper performs a comparative study to verify the performance and efficiency of the proposed controller. Robust, stable financial systems significantly improve the growth of an economic system. The stabilization of financial systems poses the following challenges. The state variables' trajectories (i) lie outside the basin of attraction, (ii) have high oscillations, and (iii) converge to the equilibrium state slowly. This paper aims to design a controller that develops a robust, stable financial closed-loop system to address the challenges above by (i) attracting all state variables to the origin, (ii) reducing the oscillations, and (iii) increasing the gradient of the convergence. This paper proposes a detailed mathematical analysis of the steady-state stability, dissipative characteristics, the Lyapunov exponents, bifurcation phenomena, and Poincare maps of chaotic financial dynamic systems. The proposed controller does not cancel the nonlinear terms appearing in the closed-loop. This structure is robust to the smoothly varying system parameters and improves closed-loop efficiency. Further, the controller eradicates the effects of inevitable exogenous disturbances and accomplishes a faster, oscillation-free convergence of the perturbed state variables to the desired steady-state within a finite time. The Lyapunov stability analysis proves the closed-loop global stability. The paper also discusses finite-time stability analysis and describes the controller parameters' effects on the convergence rates. Computer-based simulations endorse the theoretical findings, and the comparative study highlights the benefits. Theoretical analysis proofs and computer simulation results verify that the proposed controller compels the state trajectories, including trajectories outside the basin of attraction, to the origin within finite time without oscillations while being faster than the other controllers discussed in the comparative study section. This article proposes a novel robust, nonlinear finite-time controller for the robust stabilization of the chaotic finance model. It provides an in-depth analysis based on the Lyapunov stability theory and computer simulation results to verify the robust convergence of the state variables to the origin. [ABSTRACT FROM AUTHOR]
- Published
- 2021
- Full Text
- View/download PDF
10. Asymptotic stability results of generalized discrete time reaction diffusion system applied to Lengyel-Epstein and Dagn Harrison models.
- Author
-
Almatroud, Othman Abdullah, Hioual, Amel, Ouannas, Adel, and Batiha, Iqbal M.
- Subjects
- *
GLOBAL asymptotic stability , *DISCRETE systems , *COMPUTER simulation - Abstract
In this research paper, we delve into the analysis of a generalized discrete reaction-diffusion system. Our study begins with the discretization of a generalized reaction-diffusion model, achieved through second-order and L 1-difference approximations. We explore the local stability of its unique solution, both in the absence and presence of the diffusion term. To determine the conditions for global asymptotic stability of the steady-state solution, we employ suitable techniques including the direct Lyapunov method. To illustrate the practical application of this theoretical framework, we provide several numerical simulations that examine both the Lengyel-Epstein reaction-diffusion model and the discrete Degn-Harrison reaction-diffusion model. These simulations serve to validate the predictions of asymptotic stability. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
11. Fractional Grassi–Miller Map Based on the Caputo h-Difference Operator: Linear Methods for Chaos Control and Synchronization.
- Author
-
Talbi, Ibtissem, Ouannas, Adel, Grassi, Giuseppe, Khennaoui, Amina-Aicha, Pham, Viet-Thanh, and Baleanu, Dumitru
- Subjects
- *
LINEAR operators , *CHAOS synchronization , *DISCRETE systems , *LYAPUNOV functions , *CHARTS, diagrams, etc. , *POLYNOMIAL chaos , *BIFURCATION diagrams - Abstract
Investigating dynamic properties of discrete chaotic systems with fractional order has been receiving much attention recently. This paper provides a contribution to the topic by presenting a novel version of the fractional Grassi–Miller map, along with improved schemes for controlling and synchronizing its dynamics. By exploiting the Caputo h-difference operator, at first, the chaotic dynamics of the map are analyzed via bifurcation diagrams and phase plots. Then, a novel theorem is proved in order to stabilize the dynamics of the map at the origin by linear control laws. Additionally, two chaotic fractional Grassi–Miller maps are synchronized via linear controllers by utilizing a novel theorem based on a suitable Lyapunov function. Finally, simulation results are reported to show the effectiveness of the approach developed herein. [ABSTRACT FROM AUTHOR]
- Published
- 2020
- Full Text
- View/download PDF
12. Different dimensional fractional-order discrete chaotic systems based on the Caputo h-difference discrete operator: dynamics, control, and synchronization.
- Author
-
Talbi, Ibtissem, Ouannas, Adel, Khennaoui, Amina-Aicha, Berkane, Abdelhak, Batiha, Iqbal M., Grassi, Giuseppe, and Pham, Viet-Thanh
- Subjects
- *
DISCRETE systems , *SYNCHRONIZATION - Abstract
The paper investigates control and synchronization of fractional-order maps described by the Caputo h-difference operator. At first, two new fractional maps are introduced, i.e., the Two-Dimensional Fractional-order Lorenz Discrete System (2D-FoLDS) and Three-Dimensional Fractional-order Wang Discrete System (3D-FoWDS). Then, some novel theorems based on the Lyapunov approach are proved, with the aim of controlling and synchronizing the map dynamics. In particular, a new hybrid scheme is proposed, which enables synchronization to be achieved between a master system based on a 2D-FoLDS and a slave system based on a 3D-FoWDS. Simulation results are reported to highlight the effectiveness of the conceived approach. [ABSTRACT FROM AUTHOR]
- Published
- 2020
- Full Text
- View/download PDF
13. On the Three-Dimensional Fractional-Order Hénon Map with Lorenz-Like Attractors.
- Author
-
Khennaoui, Amina-Aicha, Ouannas, Adel, Odibat, Zaid, Pham, Viet-Thanh, and Grassi, Giuseppe
- Subjects
- *
POINCARE maps (Mathematics) , *STABILITY of linear systems , *DESIGN exhibitions , *BIFURCATION diagrams , *CHARTS, diagrams, etc. , *STABILITY criterion - Abstract
A three-dimensional (3D) Hénon map of fractional order is proposed in this paper. The dynamics of the suggested map are numerically illustrated for different fractional orders using phase plots and bifurcation diagrams. Lorenz-like attractors for the considered map are realized. Then, using the linear fractional-order systems stability criterion, a controller is proposed to globally stabilize the fractional-order Hénon map. Furthermore, synchronization control scheme has been designed to exhibit a synchronization behavior between a given 2D fractional-order chaotic map and the 3D fractional-order Hénon map. Numerical simulations are also performed to verify the main results of the study. [ABSTRACT FROM AUTHOR]
- Published
- 2020
- Full Text
- View/download PDF
14. A new generalized synchronization scheme to control fractional chaotic dynamical systems with different dimensions and orders.
- Author
-
Chougui, Zoulikha and Ouannas, Adel
- Subjects
- *
DYNAMICAL systems , *SYNCHRONIZATION , *FRACTIONAL programming , *IMAGE encryption - Abstract
This paper addresses the problem of generalized synchronization (GS) between different dimensional fractional order chaotic systems. Based on Laplace transform theory and fractional Lyapunov-based approach, a control method for new complex GS scheme is presented. Illustrative examples are performed to show the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]
- Published
- 2020
15. Chaos and control of a three-dimensional fractional order discrete-time system with no equilibrium and its synchronization.
- Author
-
Ouannas, Adel, Khennaoui, Amina Aicha, Momani, Shaher, Grassi, Giuseppe, and Pham, Viet-Thanh
- Subjects
- *
DISCRETE-time systems , *QUANTUM chaos , *LYAPUNOV exponents , *LINEAR orderings , *STABILITY theory , *BIFURCATION diagrams - Abstract
Chaotic systems with no equilibrium are a very important topic in nonlinear dynamics. In this paper, a new fractional order discrete-time system with no equilibrium is proposed, and the complex dynamical behaviors of such a system are discussed numerically by means of a bifurcation diagram, the largest Lyapunov exponents, a phase portrait, and a 0–1 test. In addition, a one-dimensional controller is proposed. The asymptotic convergence of the proposed controller is established by means of the stability theory of linear fractional order discrete-time systems. Next, a synchronization control scheme for two different fractional order discrete-time systems with hidden attractors is reported, where the master system is a two-dimensional system that has been reported in the literature. Numerical results are presented to confirm the results. [ABSTRACT FROM AUTHOR]
- Published
- 2020
- Full Text
- View/download PDF
16. A New Fractional Discrete Memristive Map with Variable Order and Hidden Dynamics.
- Author
-
Almatroud, Othman Abdullah, Khennaoui, Amina-Aicha, Ouannas, Adel, Alshammari, Saleh, and Albosaily, Sahar
- Subjects
- *
POINCARE maps (Mathematics) , *DIFFERENCE operators , *FRACTIONAL calculus - Abstract
This paper introduces and explores the dynamics of a novel three-dimensional (3D) fractional map with hidden dynamics. The map is constructed through the integration of a discrete sinusoidal memristive into a discrete Duffing map. Moreover, a mathematical operator, namely, a fractional variable-order Caputo-like difference operator, is employed to establish the fractional form of the map with short memory. The numerical simulation results highlight its excellent dynamical behavior, revealing that the addition of the piecewise fractional order makes the memristive-based Duffing map even more chaotic. It is characterized by distinct features, including the absence of an equilibrium point and the presence of multiple hidden chaotic attractors. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
17. On chaos in the fractional-order Grassi–Miller map and its control.
- Author
-
Ouannas, Adel, Khennaoui, Amina-Aicha, Grassi, Giuseppe, and Bendoukha, Samir
- Subjects
- *
BIFURCATION diagrams , *DISCRETE-time systems - Abstract
In this paper, we propose and examine the fractional form corresponding to the Grassi–Miller integer-order discrete-time system. We show experimental phase portraits and bifurcation diagrams to highlight the ranges of parameters and fractional orders over which chaos is observed. In addition, we propose two distinct control schemes for the proposed fractional map. The first controller stabilizes the states and forces them towards zero asymptotically. The second controller aims to synchronize a pair of maps with non-identical parameters. Throughout the paper, numerical results are presented to verify the analytic results. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
- View/download PDF
18. On the Dynamics and Control of a Fractional Form of the Discrete Double Scroll.
- Author
-
Ouannas, Adel, Khennaoui, Amina-Aicha, Bendoukha, Samir, and Grassi, Giuseppe
- Subjects
- *
BIFURCATION diagrams , *SYNCHRONIZATION - Abstract
This paper is concerned with the dynamics and control of the fractional version of the discrete double scroll hyperchaotic map. Using phase portraits and bifurcation diagrams, we show that the general behavior of the proposed map depends on the fractional order. We also present two control schemes for the proposed map, one that adaptively stabilizes the map, and another to achieve the complete synchronization of a pair of maps. Numerical results are presented to illustrate the findings. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
- View/download PDF
19. On the Q–S Chaos Synchronization of Fractional-Order Discrete-Time Systems: General Method and Examples.
- Author
-
Ouannas, Adel, Khennaoui, Amina-Aicha, Grassi, Giuseppe, and Bendoukha, Samir
- Subjects
- *
CHAOS theory , *FRACTIONAL calculus , *DISCRETE-time systems , *STABILITY theory , *SYNCHRONIZATION - Abstract
In this paper, we propose two control strategies for the Q–S synchronization of fractional-order discrete-time chaotic systems. Assuming that the dimension of the response system m is higher than that of the drive system n, the first control scheme achieves n-dimensional synchronization whereas the second deals with the m-dimensional case. The stability of the proposed schemes is established by means of the linearization method. Numerical results are presented to confirm the findings of the study. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
20. Function-based hybrid synchronization types and their coexistence in non-identical fractional-order chaotic systems.
- Author
-
Ouannas, Adel, Grassi, Giuseppe, Wang, Xiong, Ziar, Toufik, and Pham, Viet-Thanh
- Subjects
- *
CHAOS synchronization , *CHAOS theory , *FRACTIONS , *NUMERICAL analysis , *LORENZ equations - Abstract
This paper presents new results related to the coexistence of function-based hybrid synchronization types between non-identical incommensurate fractional-order systems characterized by different dimensions and orders. Specifically, a new theorem is illustrated, which ensures the coexistence of the full-state hybrid function projective synchronization (FSHFPS) and the inverse full-state hybrid function projective synchronization (IFSHFPS) between wide classes of three-dimensional master systems and four-dimensional slave systems. In order to show the capability of the approach, a numerical example is reported, which illustrates the coexistence of FSHFPS and IFSHFPS between the incommensurate chaotic fractional-order unified system and the incommensurate hyperchaotic fractional-order Lorenz system. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
21. Coexistence of identical synchronization, antiphase synchronization and inverse full state hybrid projective synchronization in different dimensional fractional-order chaotic systems.
- Author
-
Ouannas, Adel, Wang, Xiong, Pham, Viet-Thanh, Grassi, Giuseppe, and Ziar, Toufik
- Subjects
- *
SYNCHRONIZATION , *CHAOS theory , *LYAPUNOV exponents , *DIFFERENTIAL equations , *MATHEMATICAL analysis - Abstract
The topic related to the coexistence of different synchronization types between fractional-order chaotic systems is almost unexplored in the literature. Referring to commensurate and incommensurate fractional systems, this paper presents a new approach to rigorously study the coexistence of some synchronization types between nonidentical systems characterized by different dimensions and different orders. In particular, the paper shows that identical synchronization ( IS), antiphase synchronization ( AS), and inverse full state hybrid projective synchronization ( IFSHPS) coexist when synchronizing a three-dimensional master system with a fourth-dimensional slave system. The approach, which can be applied to a wide class of chaotic/hyperchaotic fractional-order systems in the master-slave configuration, is based on two new theorems involving the fractional Lyapunov method and stability theory of linear fractional systems. Two examples are provided to highlight the capability of the conceived method. In particular, referring to commensurate systems, the coexistence of IS, AS, and IFSHPS is successfully achieved between the chaotic three-dimensional Rössler system of order 2.7 and the hyperchaotic four-dimensional Chen system of order 3.84. Finally, referring to incommensurate systems, the coexistence of IS, AS, and IFSHPS is successfully achieved between the chaotic three-dimensional Lü system of order 2.955 and the hyperchaotic four-dimensional Lorenz system of order 3.86. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
22. A fractional-order form of a system with stable equilibria and its synchronization.
- Author
-
Wang, Xiong, Ouannas, Adel, Pham, Viet-Thanh, and Abdolmohammadi, Hamid Reza
- Subjects
- *
CHAOS synchronization , *STABLE equilibrium (Physics) , *NUMERICAL analysis , *MANIFOLDS (Mathematics) , *NORMAL forms (Mathematics) - Abstract
There has been an increasing interest in studying fractional-order chaotic systems and their synchronization. In this paper, the fractional-order form of a system with stable equilibrium is introduced. It is interesting that such a three-dimensional fractional system can exhibit chaotic attractors. Full-state hybrid projective synchronization scheme and inverse full-state hybrid projective synchronization scheme have been designed to synchronize the three-dimensional fractional system with different four-dimensional fractional systems. Numerical examples have verified the proposed synchronization schemes. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
23. Nonlinear methods to control synchronization between fractional-order and integer-order chaotic systems.
- Author
-
Ouannas, Adel, Zehrour, Okba, and Laadjal, Zaid
- Subjects
- *
LYAPUNOV functions , *DIFFERENTIAL equations , *CHAOS synchronization , *INTEGERS , *MATHEMATICS theorems - Abstract
In this paper, we present nonlinear methods to synchronize different dimensional master and slave chaotic systems described by integer-order and fractional-order differential equations. Based on integer-order Lyapunov stability method and fractional-order Lyapunov approach, effective control schemes to rigorously study the coexistence of generalized synchronization and inverse generalized synchronization, between integer-order and fractional-order chaotic systems with different dimensions, are introduced. Numerical examples are used to verify the effectiveness of the proposed schemes. [ABSTRACT FROM AUTHOR]
- Published
- 2018
24. COEXISTENCE OF SOME CHAOS SYNCHRONIZATION TYPES IN FRACTIONAL-ORDER DIFFERENTIAL EQUATIONS.
- Author
-
OUANNAS, ADEL, ABDELMALEK, SALEM, and BENDOUKHA, SAMIR
- Subjects
- *
SYNCHRONIZATION , *FOUR-dimensional models (String theory) , *STABILITY theory , *LYAPUNOV functions , *DIFFERENTIAL equations - Abstract
Referring to incommensurate and commensurate fractional systems, this article presents a new approach to investigate the coexistence of some synchronization types between non-identical systems characterized by different dimensions and different orders. In particular, the paper shows that complete synchronization (CS), anti-synchronization (AS) and inverse full state hybrid function projective synchronization (IFSHFPS) coexist when synchronizing a three-dimensional master system with a four-dimensional slave system. The approach is based on two new results involving stability theory of linear fractional systems and the fractional Lyapunov method. A number of examples are provided to highlight the applicability of the method. [ABSTRACT FROM AUTHOR]
- Published
- 2017
25. Universal chaos synchronization control laws for general quadratic discrete systems.
- Author
-
Ouannas, Adel, Odibat, Zaid, Shawagfeh, Nabil, Alsaedi, Ahmed, and Ahmad, Bashir
- Subjects
- *
CHAOS synchronization , *DISCRETE systems , *NONLINEAR control theory , *DYNAMICAL systems , *LYAPUNOV stability - Abstract
This paper addresses the reliable universal synchronization problem between two coupled chaotic quadratic discrete systems. A general nonlinear control method of synchronization for coupled 2D and 3D quadratic dynamical systems in discrete-time is proposed. The proposed synchronization method is based on universal controllers. The synchronization results are derived theoretically using active control method and Lyapunov stability theory. Numerical simulations are performed to assess the performance of the presented analysis. [ABSTRACT FROM AUTHOR]
- Published
- 2017
- Full Text
- View/download PDF
26. On Variable-Order Fractional Discrete Neural Networks: Solvability and Stability.
- Author
-
Hioual, Amel, Ouannas, Adel, Oussaeif, Taki-Eddine, Grassi, Giuseppe, Batiha, Iqbal M., and Momani, Shaher
- Subjects
- *
ARTIFICIAL neural networks , *ARTIFICIAL intelligence , *DEEP learning , *MULTILAYER perceptrons , *NEURO-controllers , *MATHEMATICS theorems - Abstract
Few papers have been published to date regarding the stability of neural networks described by fractional difference operators. This paper makes a contribution to the topic by presenting a variable-order fractional discrete neural network model and by proving its Ulam–Hyers stability. In particular, two novel theorems are illustrated, one regarding the existence of the solution for the proposed variable-order network and the other regarding its Ulam–Hyers stability. Finally, numerical simulations of three-dimensional and two-dimensional variable-order fractional neural networks were carried out to highlight the effectiveness of the conceived theoretical approach. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
27. On Fractional-Order Discrete-Time Reaction Diffusion Systems.
- Author
-
Almatroud, Othman Abdullah, Hioual, Amel, Ouannas, Adel, and Grassi, Giuseppe
- Subjects
- *
DIFFERENCE operators , *FRACTIONAL calculus , *DISCRETE-time systems , *SYSTEM dynamics , *MALONIC acid - Abstract
Reaction–diffusion systems have a broad variety of applications, particularly in biology, and it is well known that fractional calculus has been successfully used with this type of system. However, analyzing these systems using discrete fractional calculus is novel and requires significant research in a diversity of disciplines. Thus, in this paper, we investigate the discrete-time fractional-order Lengyel–Epstein system as a model of the chlorite iodide malonic acid (CIMA) chemical reaction. With the help of the second order difference operator, we describe the fractional discrete model. Furthermore, using the linearization approach, we established acceptable requirements for the local asymptotic stability of the system's unique equilibrium. Moreover, we employ a Lyapunov functional to show that when the iodide feeding rate is moderate, the constant equilibrium solution is globally asymptotically stable. Finally, numerical models are presented to validate the theoretical conclusions and demonstrate the impact of discretization and fractional-order on system dynamics. The continuous version of the fractional-order Lengyel–Epstein reaction–diffusion system is compared to the discrete-time system under consideration. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
28. On Variable-Order Fractional Discrete Neural Networks: Existence, Uniqueness and Stability.
- Author
-
Almatroud, Othman Abdullah, Hioual, Amel, Ouannas, Adel, Sawalha, Mohammed Mossa, Alshammari, Saleh, and Alshammari, Mohammad
- Subjects
- *
FRACTIONAL calculus , *COMPUTER simulation - Abstract
Given the recent advances regarding the studies of discrete fractional calculus, and the fact that the dynamics of discrete-time neural networks in fractional variable-order cases have not been sufficiently documented, herein, we consider a novel class of discrete-time fractional-order neural networks using discrete nabla operator of variable-order. An adequate criterion for the existence of the solution in addition to its uniqueness for such systems is provided with the use of Banach fixed point technique. Moreover, the uniform stability is investigated. We provide at the end two numerical simulations illustrating the relevance of the aforementioned results. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
29. Synchronization of the Glycolysis Reaction-Diffusion Model via Linear Control Law.
- Author
-
Ouannas, Adel, Batiha, Iqbal M., Bekiros, Stelios, Liu, Jinping, Jahanshahi, Hadi, Aly, Ayman A., and Alghtani, Abdulaziz H.
- Subjects
- *
GLYCOLYSIS , *SYNCHRONIZATION , *LYAPUNOV functions , *BIOCHEMICAL models , *DIFFUSION , *COMPUTER simulation - Abstract
The Selkov system, which is typically employed to model glycolysis phenomena, unveils some rich dynamics and some other complex formations in biochemical reactions. In the present work, the synchronization problem of the glycolysis reaction-diffusion model is handled and examined. In addition, a novel convenient control law is designed in a linear form and, on the other hand, the stability of the associated error system is demonstrated through utilizing a suitable Lyapunov function. To illustrate the applicability of the proposed schemes, several numerical simulations are performed in one- and two-spatial dimensions. [ABSTRACT FROM AUTHOR]
- Published
- 2021
- Full Text
- View/download PDF
30. The Optimal Homotopy Asymptotic Method for Solving Two Strongly Fractional-Order Nonlinear Benchmark Oscillatory Problems.
- Author
-
Shatnawi, Mohd Taib, Ouannas, Adel, Bahia, Ghenaiet, Batiha, Iqbal M., and Grassi, Giuseppe
- Subjects
- *
BENCHMARK problems (Computer science) , *NONLINEAR oscillators , *LINEAR operators - Abstract
This paper proceeds from the perspective that most strongly nonlinear oscillators of fractional-order do not enjoy exact analytical solutions. Undoubtedly, this is a good enough reason to employ one of the major recent approximate methods, namely an Optimal Homotopy Asymptotic Method (OHAM), to offer approximate analytic solutions for two strongly fractional-order nonlinear benchmark oscillatory problems, namely: the fractional-order Duffing-relativistic oscillator and the fractional-order stretched elastic wire oscillator (with a mass attached to its midpoint). In this work, a further modification has been proposed for such method and then carried out through establishing an optimal auxiliary linear operator, an auxiliary function, and an auxiliary control parameter. In view of the two aforesaid applications, it has been demonstrated that the OHAM is a reliable approach for controlling the convergence of approximate solutions and, hence, it is an effective tool for dealing with such problems. This assertion is completely confirmed by performing several graphical comparisons between the OHAM and the Homotopy Analysis Method (HAM). [ABSTRACT FROM AUTHOR]
- Published
- 2021
- Full Text
- View/download PDF
31. Multistability, Chaos, and Synchronization in Novel Symmetric Difference Equation.
- Author
-
Almatroud, Othman Abdullah, Abu Hammad, Ma'mon, Dababneh, Amer, Diabi, Louiza, Ouannas, Adel, Khennaoui, Amina Aicha, and Alshammari, Saleh
- Subjects
- *
DIFFERENCE equations , *LYAPUNOV exponents , *SYMMETRY , *ENTROPY , *SYNCHRONIZATION , *BIFURCATION diagrams - Abstract
This paper presents a new third-order symmetric difference equation transformed into a 3D discrete symmetric map. The nonlinear dynamics and symmetry of the proposed map are analyzed with two initial conditions for exploring the sensitivity of the map and highlighting the influence of the map parameters on its behaviors, thus comparing the findings. Moreover, the stability of the zero fixed point and symmetry are examined by theoretical analysis, and it is proved that the map generates diverse nonlinear traits comprising multistability, chaos, and hyperchaos, which is confirmed by phase attractors in 2D and 3D space, Lyapunov exponents ( L E s ) analysis and bifurcation diagrams; also, 0-1 test and sample entropy (SampEn) are used to confirm the existence and measure the complexity of chaos. In addition, a nonlinear controller is introduced to stabilize the symmetry map and synchronize a duo of unified symmetry maps. Finally, numerical results are provided to illustrate the findings. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
32. Modified Three-Point Fractional Formulas with Richardson Extrapolation.
- Author
-
Batiha, Iqbal M., Alshorm, Shameseddin, Ouannas, Adel, Momani, Shaher, Ababneh, Osama Y., and Albdareen, Meaad
- Subjects
- *
EXTRAPOLATION , *FRACTIONAL calculus , *VALUES (Ethics) - Abstract
In this paper, we introduce new three-point fractional formulas which represent three generalizations for the well-known classical three-point formulas; central, forward and backward formulas. This has enabled us to study the function's behavior according to different fractional-order values of α numerically. Accordingly, we then introduce a new methodology for Richardson extrapolation depending on the fractional central formula in order to obtain a high accuracy for the gained approximations. We compare the efficiency of the proposed methods by using tables and figures to show their reliability. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
33. A New Incommensurate Fractional-Order Discrete COVID-19 Model with Vaccinated Individuals Compartment.
- Author
-
Dababneh, Amer, Djenina, Noureddine, Ouannas, Adel, Grassi, Giuseppe, Batiha, Iqbal M., and Jebril, Iqbal H.
- Subjects
- *
VACCINATION , *COVID-19 , *COVID-19 pandemic , *BASIC reproduction number , *DIFFERENCE equations , *EPIDEMICS - Abstract
Fractional-order systems have proved to be accurate in describing the spread of the COVID-19 pandemic by virtue of their capability to include the memory effects into the system dynamics. This manuscript presents a novel fractional discrete-time COVID-19 model that includes the number of vaccinated individuals as an additional state variable in the system equations. The paper shows that the proposed compartment model, described by difference equations, has two fixed points, i.e., a disease-free fixed point and an epidemic fixed point. A new theorem is proven which highlights that the pandemic disappears when an inequality involving the percentage of the population in quarantine is satisfied. Finally, numerical simulations are carried out to show that the proposed incommensurate fractional-order model is effective in describing the spread of the COVID-19 pandemic. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
34. A Nonlinear Fractional Problem with a Second Kind Integral Condition for Time-Fractional Partial Differential Equation.
- Author
-
Abdelouahab, Benbrahim, Oussaeif, Taki-Eddine, Ouannas, Adel, Saad, Khaled M., Jahanshahi, Hadi, Diar, Ahmed, Aljuaid, Awad M., and Aly, Ayman A.
- Subjects
- *
PARTIAL differential equations , *NONLINEAR equations , *INTEGRALS - Abstract
The aim of this research is to demonstrate the existence and the uniqueness of the weak solution for a semilinear fractional parabolic problem with the special case of the second integral boundary condition. For this aim, we split the proof into two parts; to study the main linear problem part, we used the variable separation method, and concerning the semilinear problem part, we apply an iterative method and a priori estimate for the study of the weak solution. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
35. On the Stability of Linear Incommensurate Fractional-Order Difference Systems.
- Author
-
Djenina, Noureddine, Ouannas, Adel, Batiha, Iqbal M., Grassi, Giuseppe, and Pham, Viet-Thanh
- Subjects
- *
DIFFERENCE equations , *VOLTERRA equations - Abstract
To follow up on the progress made on exploring the stability investigation of linear commensurate Fractional-order Difference Systems (FoDSs), such topic of its extended version that appears with incommensurate orders is discussed and examined in this work. Some simple applicable conditions for judging the stability of these systems are reported as novel results. These results are formulated by converting the linear incommensurate FoDS into another equivalent system consists of fractional-order difference equations of Volterra convolution-type as well as by using some properties of the Z-transform method. All results of this work are verified numerically by illustrating some examples that deal with the stability of solutions of such systems. [ABSTRACT FROM AUTHOR]
- Published
- 2020
- Full Text
- View/download PDF
36. Bifurcations, Hidden Chaos and Control in Fractional Maps.
- Author
-
Ouannas, Adel, Almatroud, Othman Abdullah, Khennaoui, Amina Aicha, Alsawalha, Mohammad Mossa, Baleanu, Dumitru, Huynh, Van Van, and Pham, Viet-Thanh
- Subjects
- *
NONLINEAR dynamical systems , *POINCARE maps (Mathematics) , *BIFURCATION diagrams , *CHAOS theory , *FRACTIONAL calculus - Abstract
Recently, hidden attractors with stable equilibria have received considerable attention in chaos theory and nonlinear dynamical systems. Based on discrete fractional calculus, this paper proposes a simple two-dimensional and three-dimensional fractional maps. Both fractional maps are chaotic and have a unique equilibrium point. Results show that the dynamics of the proposed fractional maps are sensitive to both initial conditions and fractional order. There are coexisting attractors which have been displayed in terms of bifurcation diagrams, phase portraits and a 0-1 test. Furthermore, control schemes are introduced to stabilize the chaotic trajectories of the two novel systems. [ABSTRACT FROM AUTHOR]
- Published
- 2020
- Full Text
- View/download PDF
37. On Two-Dimensional Fractional Chaotic Maps with Symmetries.
- Author
-
Hadjabi, Fatima, Ouannas, Adel, Shawagfeh, Nabil, Khennaoui, Amina-Aicha, and Grassi, Giuseppe
- Subjects
- *
BIFURCATION diagrams , *SYMMETRY , *ATTRACTORS (Mathematics) - Abstract
In this paper, we propose two new two-dimensional chaotic maps with closed curve fixed points. The chaotic behavior of the two maps is analyzed by the 0–1 test, and explored numerically using Lyapunov exponents and bifurcation diagrams. It has been found that chaos exists in both fractional maps. In addition, result shows that the proposed fractional maps shows the property of coexisting attractors. [ABSTRACT FROM AUTHOR]
- Published
- 2020
- Full Text
- View/download PDF
38. A Nonlinear Fractional Problem with a Second Kind Integral Condition for Time-Fractional Partial Differential Equation.
- Author
-
Abdelwahb, Benbrahime, Oussaeif, Taki-Eddine, Ouannas, Adel, Saad, Khaled M., Jahanshahi, Hadi, Diar, Ahmed, Aljuaid, Awad M., and Aly, Ayman A.
- Subjects
- *
PARTIAL differential equations , *NONLINEAR equations , *INTEGRALS - Abstract
The aim of this research is to demonstrate the existence and the uniqueness of the weak solution for a semilinear fractional parabolic problem with the special case of the second integral boundary condition. For this aim, we split the proof into two parts; to study the main linear problem part, we used the variable separation method, and concerning the semilinear problem part, we apply an iterative method and a priori estimate for the study of the weak solution. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
39. Existence and Uniqueness of the Solution for an Inverse Problem of a Fractional Diffusion Equation with Integral Condition.
- Author
-
Oussaeif, Taki-Eddine, Antara, Benaoua, Ouannas, Adel, Batiha, Iqbal M., Saad, Khaled M., Jahanshahi, Hadi, Aljuaid, Awad M., and Aly, Ayman A.
- Subjects
- *
INTEGRAL equations , *HEAT equation , *PARTIAL differential equations , *FRACTIONAL differential equations - Abstract
The solvability of the fractional partial differential equation with integral overdetermination condition for an inverse problem is investigated in this paper. We analyze the direct problem solution by using the "energy inequality" method. Using the fixed point technique, the existence and uniqueness of the solution of the inverse problem on the data are established. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
40. On New Symmetric Fractional Discrete-Time Systems: Chaos, Complexity, and Control.
- Author
-
Hammad, Ma'mon Abu, Diabi, Louiza, Dababneh, Amer, Zraiqat, Amjed, Momani, Shaher, Ouannas, Adel, and Hioual, Amel
- Subjects
- *
BIFURCATION diagrams , *LYAPUNOV exponents , *DISCRETE-time systems , *FRACTIONAL calculus , *CHAOS theory - Abstract
This paper introduces a new symmetric fractional-order discrete system. The dynamics and symmetry of the suggested model are studied under two initial conditions, mainly a comparison of the commensurate order and incommensurate order maps, which highlights their effect on symmetry-breaking bifurcations. In addition, a theoretical analysis examines the stability of the zero equilibrium point. It proves that the map generates typical nonlinear features, including chaos, which is confirmed numerically: phase attractors are plotted in a two-dimensional (2D) and three-dimensional (3D) space, bifurcation diagrams are drawn with variations in the derivative fractional values and in the system parameters, and we calculate the Maximum Lyapunov Exponents (MLEs) associated with the bifurcation diagram. Additionally, we use the C 0 algorithm and entropy approach to measure the complexity of the chaotic symmetric fractional map. Finally, nonlinear 3D controllers are revealed to stabilize the symmetric fractional order map's states in commensurate and incommensurate cases. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
41. Comparative Analysis of Bilinear Time Series Models with Time-Varying and Symmetric GARCH Coefficients: Estimation and Simulation.
- Author
-
Abu Hammad, Ma'mon, Alkhateeb, Rami, Laiche, Nabil, Ouannas, Adel, and Alshorm, Shameseddin
- Subjects
- *
LEAST squares , *WHITE noise , *GARCH model , *COMPARATIVE studies , *TIME series analysis , *SAMPLE size (Statistics) - Abstract
This paper makes a significant contribution by focusing on estimating the coefficients of a sample of non-linear time series, a subject well-established in the statistical literature, using bilinear time series. Specifically, this study delves into a subset of bilinear models where Generalized Autoregressive Conditional Heteroscedastic (GARCH) models serve as the white noise component. The methodology involves applying the Klimko–Nilsen theorem, which plays a crucial role in extracting the asymptotic behavior of the estimators. In this context, the Generalized Autoregressive Conditional Heteroscedastic model of order (1,1) noted that the GARCH (1,1) model is defined as the white noise for the coefficients of the example models. Notably, this GARCH model satisfies the condition of having time-varying coefficients. This study meticulously outlines the essential stationarity conditions required for these models. The estimation of coefficients is accomplished by applying the least squares method. One of the key contributions lies in utilizing the fundamental theorem of Klimko and Nilsen, to prove the asymptotic behavior of the estimators, particularly how they vary with changes in the sample size. This paper illuminates the impact of estimators and their approximations based on varying sample sizes. Extending our study to include the estimation of bilinear models alongside GARCH and GARCH symmetric coefficients adds depth to our analysis and provides valuable insights into modeling financial time series data. Furthermore, this study sheds light on the influence of the GARCH white noise trace on the estimation of model coefficients. The results establish a clear connection between the model characteristics and the nature of the white noise, contributing to a more profound understanding of the relationship between these elements. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
42. Chaos, control, and synchronization in some fractional-order difference equations.
- Author
-
Khennaoui, Amina-Aicha, Ouannas, Adel, Bendoukha, Samir, Grassi, Giuseppe, Wang, Xiong, Pham, Viet-Thanh, and Alsaadi, Fawaz E.
- Subjects
- *
DIFFERENCE equations , *BIFURCATION diagrams , *SYNCHRONIZATION , *STABILITY theory , *DISCRETE systems , *FRACTIONAL calculus - Abstract
In this paper, we propose three fractional chaotic maps based on the well known 3D Stefanski, Rössler, and Wang maps. The dynamics of the proposed fractional maps are investigated experimentally by means of phase portraits, bifurcation diagrams, and Lyapunov exponents. In addition, three control laws are introduced for these fractional maps and the convergence of the controlled states towards zero is guaranteed by means of the stability theory of linear fractional discrete systems. Furthermore, a combined synchronization scheme is introduced whereby the fractional Rössler map is considered as a drive system with the response system being a combination of the remaining two maps. Numerical results are presented throughout the paper to illustrate the findings. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
- View/download PDF
43. Synchronization results for a class of fractional-order spatiotemporal partial differential systems based on fractional Lyapunov approach.
- Author
-
Ouannas, Adel, Wang, Xiong, Pham, Viet-Thanh, Grassi, Giuseppe, and Huynh, Van Van
- Subjects
- *
SYNCHRONIZATION , *NEUMANN boundary conditions - Abstract
In this paper, the problem of synchronization of a class of spatiotemporal fractional-order partial differential systems is studied. Subject to homogeneous Neumann boundary conditions and using fractional Lyapunov approach, nonlinear and linear control schemes have been proposed to synchronize coupled general fractional reaction–diffusion systems. As a numerical application, we investigate complete synchronization behaviors of coupled fractional Lengyel–Epstein systems. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
- View/download PDF
44. Synchronisation of integer-order and fractional-order discrete-time chaotic systems.
- Author
-
Ouannas, Adel, Khennaoui, Amina-Aicha, Zehrour, Okba, Bendoukha, Samir, Grassi, Giuseppe, and Pham, Viet-Thanh
- Subjects
- *
DISCRETE-time systems , *STABILITY theory , *LYAPUNOV stability , *DIFFERENCE equations , *LINEAR operators - Abstract
This paper studies the synchronisation of integer- and fractional-order discrete-time chaotic systems with different dimensions. Control laws are proposed for the full-state hybrid projective synchronisation (FSHPS) of a master–slave pair, where the difference equations of the master have an integer order while those of the slave have a fractional order. Moreover, inverse FSHPS laws are proposed for a fractional-order master and an integer-order slave. The Lyapunov stability theory of integer-order maps and the stability theory of linear fractional-order maps are utilised to establish the asymptotic stability of the zero equilibrium corresponding to the synchronisation error system. Numerical results are presented to verify the findings of the study. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
- View/download PDF
45. The fractional form of a new three-dimensional generalized Hénon map.
- Author
-
Jouini, Lotfi, Ouannas, Adel, Khennaoui, Amina-Aicha, Wang, Xiong, Grassi, Giuseppe, and Pham, Viet-Thanh
- Subjects
- *
LYAPUNOV exponents , *BIFURCATION diagrams , *FRACTIONAL calculus - Abstract
In this paper, we propose a fractional form of a new three-dimensional generalized Hénon map and study the existence of chaos and its control. Using bifurcation diagrams, phase portraits and Lyapunov exponents, we show that the general behavior of the proposed fractional map depends on the fractional order. We also present two control schemes for the proposed map, one that adaptively stabilizes the fractional map, and another to achieve the synchronization of the proposed fractional map. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
- View/download PDF
46. Chaotic Map with No Fixed Points: Entropy, Implementation and Control.
- Author
-
Huynh, Van Van, Ouannas, Adel, Wang, Xiong, Pham, Viet-Thanh, Nguyen, Xuan Quynh, and Alsaadi, Fawaz E.
- Subjects
- *
CHAOS theory , *ENTROPY (Information theory) , *FIXED point theory , *BIFURCATION diagrams , *MICROCONTROLLERS - Abstract
A map without equilibrium has been proposed and studied in this paper. The proposed map has no fixed point and exhibits chaos. We have investigated its dynamics and shown its chaotic behavior using tools such as return map, bifurcation diagram and Lyapunov exponents' diagram. Entropy of this new map has been calculated. Using an open micro-controller platform, the map is implemented, and experimental observation is presented. In addition, two control schemes have been proposed to stabilize and synchronize the chaotic map. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
- View/download PDF
47. Study of a Superlinear Problem for a Time Fractional Parabolic Equation Under Integral Over-determination Condition.
- Author
-
Batiha, Iqbal M., Benguesmia, Amal, Oussaeif, Taki-Eddine, Jebril, Iqbal H., Ouannas, Adel, and Momani, Shaher
- Subjects
- *
INTEGRAL equations , *EXISTENCE theorems , *NONLINEAR equations , *INVERSE problems , *EQUATIONS , *FUNCTIONAL analysis - Abstract
The main purpose of this paper is to examine the inverse problem associated with determining the right-hand side of a nonlinear fractional parabolic equation. This equation is accompanied by an integral over-determination supplementary condition. With the use of the functional analysis method, we establish the continuity, existence and uniqueness based on the construction of the direct problem. Such a method relies on the density of the range of the operator established for the problem at hand coupled with the energy inequality scheme. This scheme, also referred to as the method of a priori estimates, allows us to derive the existence theorem from the solution of the given problem, starting with the uniqueness theorem. For the solvability of the inverse problem and its uniqueness, we establish certain suitable conditions, and to demonstrate the existence and uniqueness of its solution, we utilize the fixed point theorem. [ABSTRACT FROM AUTHOR]
- Published
- 2024
48. Fractional Form of a Chaotic Map without Fixed Points: Chaos, Entropy and Control.
- Author
-
Ouannas, Adel, Wang, Xiong, Khennaoui, Amina-Aicha, Bendoukha, Samir, Pham, Viet-Thanh, and Alsaadi, Fawaz E.
- Subjects
- *
ENTROPY , *CHAOS theory , *FIXED point theory , *BIFURCATION diagrams , *FRACTIONAL calculus - Abstract
In this paper, we investigate the dynamics of a fractional order chaotic map corresponding to a recently developed standard map that exhibits a chaotic behavior with no fixed point. This is the first study to explore a fractional chaotic map without a fixed point. In our investigation, we use phase plots and bifurcation diagrams to examine the dynamics of the fractional map and assess the effect of varying the fractional order. We also use the approximate entropy measure to quantify the level of chaos in the fractional map. In addition, we propose a one-dimensional stabilization controller and establish its asymptotic convergence by means of the linearization method. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
49. The Co-existence of Different Synchronization Types in Fractional-order Discrete-time Chaotic Systems with Non–identical Dimensions and Orders.
- Author
-
Bendoukha, Samir, Ouannas, Adel, Wang, Xiong, Khennaoui, Amina-Aicha, Pham, Viet-Thanh, Grassi, Giuseppe, and Huynh, Van Van
- Subjects
- *
SYNCHRONIZATION , *FRACTIONAL calculus , *DISCRETE-time systems , *NONLINEAR control theory , *CHAOS theory - Abstract
This paper is concerned with the co-existence of different synchronization types for fractional-order discrete-time chaotic systems with different dimensions. In particular, we show that through appropriate nonlinear control, projective synchronization (PS), full state hybrid projective synchronization (FSHPS), and generalized synchronization (GS) can be achieved simultaneously. A second nonlinear control scheme is developed whereby inverse full state hybrid projective synchronization (IFSHPS) and inverse generalized synchronization (IGS) are shown to co-exist. Numerical examples are presented to confirm the findings. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
50. Generalized and inverse generalized synchronization of fractional-order discrete-time chaotic systems with non-identical dimensions.
- Author
-
Khennaoui, Amina-Aicha, Ouannas, Adel, Bendoukha, Samir, Grassi, Giuseppe, Wang, Xiong, and Pham, Viet-Thanh
- Subjects
- *
DISCRETE-time systems , *GENERALIZABILITY theory , *CHAOS theory , *FRACTIONAL calculus , *DIMENSIONS - Abstract
In this paper, we introduce two approaches to the generalized synchronized synchronization and the inverse generalized synchronization of fractional discrete-time chaotic systems with non-identical dimensions. The convergence of the proposed approaches is established by means of recently developed stability theory. Numerical results are presented based on well-known maps in the literature. Two examples are considered: a 3D generalized synchronization and a 2D inverse generalized synchronization. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
Catalog
Discovery Service for Jio Institute Digital Library
For full access to our library's resources, please sign in.